The couple - who have two other children, seven-year-old son Caspar and five-year-old daughter Clementine - wanted to wait until "the whole family met the newborn" before they announced her name to the world.

Cosima is an Italian name derived from the Greek word kosmos which means "order or decency". In the 2007 book 'The Baby Names Bible', written by Pamela Redmond Satran and Linda Rosenkrantz, it was described as a fashionable name for the daughters of members of high society in the UK.

Although she lives in England, Claudia recently revealed she wants to spend some time in her native Germany with her family when Matthew is working on the new 'X-Men' movie.

The catwalk beauty - who married Matthew in 2002 - said: "I would like to move to Berlin with Matthew and the kids for a few months. If we're lucky he'll be shooting some of 'X-Men' in Berlin. I would love that. Berlin is like being abroad in Germany. It's German, but not provincial. Everyone loves it. My friends often tell me how very German I still am."